A method for calculating the dispersion of guided waves in pipe

A finite element based mode analysis method is proposed to solve the dispersion relations. Based on the guided wave theory, the Navier stokes equation is constructed. The Helmholtz equation and functional form are obtained by using the variable separation method and solved by the finite element method. The calculated results are basically consistent with the results obtained by the semi-analytical finite element method, and the ring modal can be gotten, which proves the effectiveness and comprehensiveness of this method. At the same time, the guided wave theory and the Timoshenko Beam theory are applied to theoretically solve the dispersion relations of low frequency, which shows the characteristics of the modal analysis method are superior. Finally, the modal characteristics are analyzed by the displacement component, which provides a basis for the mode selection of guided wave on nondestructive testing.